Resources tagged with: Generalising

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There are 140 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising

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Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

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Got It

Age 7 to 14 Challenge Level:

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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Got it for Two

Age 7 to 14 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

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Number Pyramids

Age 11 to 14 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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Button-up Some More

Age 7 to 11 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Make 37

Age 7 to 14 Challenge Level:

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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Crossings

Age 7 to 11 Challenge Level:

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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Domino Numbers

Age 7 to 11 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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More Number Pyramids

Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Partitioning Revisited

Age 11 to 14 Challenge Level:

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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Broken Toaster

Age 7 to 11 Short Challenge Level:

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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Maths Trails

Age 7 to 14

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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Nim-7

Age 5 to 14 Challenge Level:

Can you work out how to win this game of Nim? Does it matter if you go first or second?

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Dotty Circle

Age 7 to 11 Challenge Level:

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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Window Frames

Age 5 to 14 Challenge Level:

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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Sitting Round the Party Tables

Age 5 to 11 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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More Magic Potting Sheds

Age 11 to 14 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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What Numbers Can We Make Now?

Age 11 to 14 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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Walking the Squares

Age 7 to 11 Challenge Level:

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

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Play to 37

Age 7 to 11 Challenge Level:

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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Build it Up

Age 7 to 11 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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Round and Round the Circle

Age 7 to 11 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Konigsberg Plus

Age 11 to 14 Challenge Level:

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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Triangle Pin-down

Age 7 to 11 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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Build it up More

Age 7 to 11 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

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Truth or Lie

Age 7 to 11 Challenge Level:

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

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Tumbling Down

Age 7 to 11 Challenge Level:

Watch this animation. What do you see? Can you explain why this happens?

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Centred Squares

Age 7 to 11 Challenge Level:

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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Winning Lines

Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

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Tourism

Age 11 to 14 Challenge Level:

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

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Go Forth and Generalise

Age 11 to 14

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

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Frogs

Age 11 to 14 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method?

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Odd Squares

Age 7 to 11 Challenge Level:

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

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Picturing Square Numbers

Age 11 to 14 Challenge Level:

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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Circles, Circles

Age 5 to 11 Challenge Level:

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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Steps to the Podium

Age 7 to 14 Challenge Level:

It starts quite simple but great opportunities for number discoveries and patterns!

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Special Sums and Products

Age 11 to 14 Challenge Level:

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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What Numbers Can We Make?

Age 11 to 14 Challenge Level:

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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Sums and Differences 1

Age 7 to 11 Challenge Level:

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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Sums and Differences 2

Age 7 to 11 Challenge Level:

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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Three Dice

Age 7 to 11 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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Surprising Split

Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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Division Rules

Age 7 to 11 Challenge Level:

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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Christmas Chocolates

Age 11 to 14 Challenge Level:

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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Always, Sometimes or Never?

Age 5 to 11 Challenge Level:

Are these statements relating to odd and even numbers always true, sometimes true or never true?

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Roll over the Dice

Age 7 to 11 Challenge Level:

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

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Nim-7 for Two

Age 5 to 14 Challenge Level:

Nim-7 game for an adult and child. Who will be the one to take the last counter?

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Strike it Out for Two

Age 5 to 11 Challenge Level:

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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Handshakes

Age 11 to 14 Challenge Level:

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?